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<div class="iris_headline">IRIS Toolbox Reference Manual</div>




<h2 id="model/sspace">sspace</h2>
<div class="headline">State-space matrices describing the model solution</div>

<h4 id="syntax">Syntax</h4>
<pre><code>[T,R,K,Z,H,D,U,Omg] = sspace(m,...)</code></pre>
<h4 id="input-arguments">Input arguments</h4>
<ul>
<li><code>m</code> [ model ] - Solved model object.</li>
</ul>
<h4 id="output-arguments">Output arguments</h4>
<ul>
<li><p><code>T</code> [ numeric ] - Transition matrix.</p></li>
<li><p><code>R</code> [ numeric ] - Matrix at the shock vector in transition equations.</p></li>
<li><p><code>K</code> [ numeric ] - Constant vector in transition equations.</p></li>
<li><p><code>Z</code> [ numeric ] - Matrix mapping transition variables to measurement variables.</p></li>
<li><p><code>H</code> [ numeric ] - Matrix at the shock vector in measurement equations.</p></li>
<li><p><code>D</code> [ numeric ] - Constant vector in measurement equations.</p></li>
<li><p><code>U</code> [ numeric ] - Transformation matrix for predetermined variables.</p></li>
<li><p><code>Omg</code> [ numeric ] - Covariance matrix of shocks.</p></li>
</ul>
<h4 id="options">Options</h4>
<ul>
<li><code>'triangular='</code> [ <em><code>true</code></em> | <code>false</code> ] - If true, the state-space form returned has the transition matrix <code>T</code> quasi triangular and the vector of predetermined variables transformed accordingly; this is the form used in IRIS calculations. If false, the state-space system refers to the original vector of transition variables.</li>
</ul>
<h4 id="description">Description</h4>
<p>The state-space representation has the following form:</p>
<pre><code>[xf;alpha] = T*alpha(-1) + K + R*e

y = Z*alpha + D + H*e

xb = U*alpha

Cov[e] = Omg</code></pre>
<p>where <code>xb</code> is an nb-by-1 vector of predetermined (backward-looking) transition variables and their auxiliary lags, <code>xf</code> is an nf-by-1 vector of non-predetermined (forward-looking) variables and their auxiliary leads, <code>alpha</code> is a transformation of <code>xb</code>, <code>e</code> is an ne-by-1 vector of shocks, and <code>y</code> is an ny-by-1 vector of measurement variables. Furthermore, we denote the total number of transition variables, and their auxiliary lags and leads, nx = nb + nf.</p>
<p>The transition matrix, <code>T</code>, is, in general, rectangular nx-by-nb. Furthremore, the transformed state vector alpha is chosen so that the lower nb-by-nb part of <code>T</code> is quasi upper triangular.</p>
<p>You can use the <code>get(m,'xVector')</code> function to learn about the order of appearance of transition variables and their auxiliary lags and leads in the vectors <code>xb</code> and <code>xf</code>. The first nf names are the vector <code>xf</code>, the remaining nb names are the vector <code>xb</code>.</p>

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<div class="copyright">IRIS Toolbox. Copyright &copy; 2007-2014 Jaromir Benes.</div>
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